The Italian is in the final year of his contract at the Stadio Olimpico and could leave the club for less than his £15 million valuation.
Roma director Walter Sabattini has already admitted the Serie A club may have to sell their star midfielder and that has caused interest in the 27-year-old to soar.
New boss Luis Enrique wants to hold onto De Rossi who he sees as a vital part of his new team.
“He is very important for my plans and it would be impossible to find a replacement for him in the current market.” He told The Mirror
Chelsea are in the hunt for an experienced holding midfielder after losing Michael Essien for six months to another knee injury and De Rossi fits the bill.
A move for West Ham’s Scott Parker has been mooted but new boss Andre Villas-Boas wants a midfielder with a European pedigree.
Interest from City is also high, as they want to strengthen their midfield before they embark on their first ever Champions League campaign.
With both clubs carrying a hefty war chest any move for the player could descend into a bidding war.